Known commercial satellites collect multispectral bands at a lower resolution than the panchromatic band. The WorldView-2 (WV-2) satellite, launched by DigitalGlobe on Oct. 8, 2009 represents the first commercial imaging satellite to collect very high spatial resolution data in 8 spectral bands. The multispectral bands cover the spectral range from 400 nm-1050 nm at a 1.84 m spatial resolution, while the panchromatic band covers the spectrum from 450 nm-800 nm with 4× greater spatial resolution, 0.46 m. The relative spectral responses from each band are shown in FIG. 1.
It is often desired to have the high spatial resolution and the high spectral resolution information combined in the same file. Pan-sharpening is a type of data fusion that refers to the process of combining the lower-resolution color pixels with the higher resolution panchromatic pixels to produce a high resolution color image. Pan-sharpening techniques are known in the art. See, for example, Nikolakopoulos, K. G, Comparison of Nine Fusion Techniques For Very High Resolution Data, PE&RS, May 2008, incorporated herein by reference. One class of techniques for pan-sharpening is called “component substitution,” where generally involves the following steps:                Upsampling: the multispectral pixels are upsampled to the same resolution as the panchromatic band (which may require data alignment when the multispectral images are not obtained from the same sensor as the panchromatic images).        Forward Transform: the upsampled multispectral pixels are transformed from the original values to a new representation, which is usually a new color space where intensity is orthogonal to the color information.        Intensity Matching: the multispectral intensity is matched to the panchromatic intensity in the transformed space. Often a histogram-matching process is employed to minimize the differences between the panchromatic intensity and the component being replaced.        Reverse Transform: the reverse transformation is performed using the substituted intensity component to transform back to the original color space.        
In cases where the multispectral and panchromatic intensities are perfectly interchangeable, the resulting imagery will have the same sharpness as the original panchromatic image as well as the same colors as the original multispectral image. In practice, however, it is often impossible to meet both of these goals and one often trades sharpness for color recovery or vice-versa. A significant factor that affects the color recovery in the resulting image is how well the forward transformation models the relationship between the panchromatic and multispectral bands.
A very simple component substitution technique for pan-sharpening is called the Hue-Intensity-Saturation (HIS) sharpening technique, which utilizes the well-known HIS color space. The conversion from the RGB color space to HIS color space is described in Tu, T. M., Huang, P. S., Hung, C. L., Chang, C. P., A Fast Intensity-Hue-Saturation Fusion Technique With spectral Adjustment for IKONOS Imagery, IEEE Geoscience and Remote Sensing Letters, Vol 1, No 4, October 2004, incorporated herein by reference. The HIS color space has the advantage that the three components are orthogonal, thus manipulating one component does not affect the other components. In the HIS color space, the intensity component (“I”) is a simple average of the three color components:
                    I        =                              1            3                    ⁢                      (                          R              +              G              +              B                        )                                              Equation        ⁢                                  ⁢        1            where R indicates the pixel value for the red band, G indicates the pixel value for the green band, and B indicates the pixel value for the blue band. However, the multispectral intensity as represented above can be a poor match for the panchromatic band, even after intensity matching is applied, resulting in poor color reproduction in the sharpened image, as is described in Tu, T. M., Su, S. C., Shyu, H. C., Huang, P. S., A new look at HIS-like image fusion methods, Information Fusion 2, (2001), 177-186, incorporated herein by reference.
In most cases, the panchromatic intensity is not modeled well by this equation, and the resulting color distortion makes the resulting product undesirable. There are two main reasons why the HIS method does not work well for these images:                The HSI model presumes a single device dependent wavelength for each of R, G and B when defining the transformation RGB to HSI, while the imagery is taken with sensors responding to bands of wavelengths in each of the R, G, and B regions (i.e., the HSI transformation assumes an infinitely narrow color response);        The HIS model only includes the values of the R, G, and B bands in the transformation, while the imagery may include more bands of color information, e.g., the QuickBird images also include Near IR information.        
As shown in FIG. 1 and FIG. 2, the multispectral coverage of the red, green, and blue bands does not cover the full spectrum of the panchromatic band for the WV-2 and QuickBird satellites. In this case a simple component substitution technique is expected to suffer from some color distortion. As described in Strait, M., Rahmani, S., Markurjev, D., Wittman, T. August 2008, Evaluation of Pan-Sharpening Methods, Technical Report, UCLA Department of Mathematics, to minimize this color distortion, it is possible to model the panchromatic intensity from the multispectral bands and employ an equation as follows:
                              I          k                =                              ∑                          i              =              1                        N                    ⁢                                    C              i                        ⁢                          MS              ik                                                          Equation        ⁢                                  ⁢        2            where k indicates a specific pixel in the image, MSik indicates the multispectral pixel for band i and location k in the image (typically derived from the upsampled image, at the same native resolution image as the panchromatic band), I is a “model” of the panchromatic band, and C is a vector of constants.
The constants, C, can be computed by statistical means. One problem with the technique, however, is that the determination of these constants is often time consuming as it may require a lot of computation. For example, the full pan-multispectral covariance matrix is required to be computed in Zhang, Y., Understanding Image Fusion, Photogrammetric Engineering and Remote Sensing, 70(6):657-661, 2004, the contents of which are incorporated herein by reference. The constants can also be determined by computing the exact spectral overlap of each multispectral band with the panchromatic band. In this case the constants must be computed separately for each sensor under consideration and this requires access to the detailed spectral response curves from the satellite provider, and such information may not be readily available.